%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM228-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:16:18 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.52s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 8 unt; 0 def)
% Number of atoms : 18 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 7 ( 1 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_2,axiom,
recursion_equation_functions(z) != null_class,
file('theBenchmark.p',prove_corollary_2) ).
cnf(c_53,plain,
recursion_equation_functions(z) != null_class,
inference(clausify,[status(thm)],[prove_corollary_2]) ).
fof(prove_corollary_1,axiom,
~ function(z),
file('theBenchmark.p',prove_corollary_1) ).
cnf(c_54,plain,
~ function(z),
inference(clausify,[status(thm)],[prove_corollary_1]) ).
fof(recursion_equation_functions1,axiom,
! [VAR_0,VAR_1] :
( function(VAR_1)
| ~ member(VAR_0,recursion_equation_functions(VAR_1)) ),
file('theBenchmark.p',recursion_equation_functions1) ).
cnf(c_68,plain,
( function(B)
| ~ member(A,recursion_equation_functions(B)) ),
inference(clausify,[status(thm)],[recursion_equation_functions1]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_132,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_133,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_132]) ).
cnf(c_693,plain,
null_class != recursion_equation_functions(z),
inference(copy,[status(thm)],[c_53]) ).
cnf(c_229,plain,
member(regular(recursion_equation_functions(z)),recursion_equation_functions(z)),
inference(resolve,[status(thm)],[c_133,c_693]) ).
cnf(c_694,plain,
function(z),
inference(resolve,[status(thm)],[c_229,c_68]) ).
cnf(c_692,plain,
$false,
inference(resolve,[status(thm)],[c_54,c_694]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM228-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n014.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 02:15:02 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.39 % Process 1895730 was started by sandbox2 on n014,
% 0.13/0.39 % Sat Sep 26 02:15:02 2026
% 0.13/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 0.17/0.52
% 0.17/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.52
% 0.17/0.52 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.17/0.52 % Length of proof is 7.
% 0.17/0.52 % Level of proof is 3.
% 0.17/0.52 % Maximum clause weight is 21.000.
% 0.17/0.52 % Given clauses 169.
% 0.17/0.52
% 0.17/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------